How do I create a 10-sided die as one object?
Fastest manual method for me so far, can be done under a minute with ease (faster if the settings in operators have been pre-saved):


Add a Cone with such settings:


Select the base vertices (Z for wireframe mode), move them 1.0 units up in Z, hit . for 3D cursor Pivot center, duplicate all with CtrlD and rotate with R 180°. Remove doubles with W5. This is what you should have:


Select every other vertex on the perimeter and the bottom vertex. Move 0.19 units up in Z.


Select all faces, hit AltJ to merge to quads. For Max Shape Angle input 50°:


Center the thing in object mode with CtrlShiftAltC Origin To Geometry and AltG. You are done with the dice: